If the message header says Time Bonus there is little point in opening it unless you have multiple missions in that system and so need to check which one to finish first.Sometimes you also get updates to missions during flight, usually when you reach the target system. For courier missions (those are missions in the game that deliver data with no cargo capacity requires) that's usually a time bonus. This is seen in the chat window, second tab. On PC default 2 for the chat window, then E/Q to change to the second tab and S to scroll down to the information, and space-bar to open it.
If it says something like Enemy Inbound then it will just have an ID and the reward for killing them which is only useful if you are in a combat build.
In my play style these messages are usually a distraction as generally I am not doing missions for credits.